It precomputes sums of all rows and columns in a 2d array for fast O(1)
querying of sums of areas within it.
It does this:
rust,ignore
let mut sum = 0;
for row in y1..y2 {
for col in x1..x2 {
sum += input[col + row * width];
}
}
but faster:
```rust,ignore // precompute let s = SummedArea::new(input, width);
// now it's fast: let sum = s.sum_range(x1..x2, y1..y2); ```